Computer simulations of the quantum dynamics of proton transfer in water and heterogeneous electron transfer processes at the electrode-electrolyte interface are proposed. In the proton transfer simulation, the protons of the water and the transferring proton will be treated quantum mechanically using the Feynman path integral representation. The computational method used is a novel quantum dynamical method developed in our group and is based on the Feynman centroid density. The simulation algorithm to be implemented combines molecular dynamics and Monte Carlo. Path integral molecular dynamics simulations are also proposed for the study of adiabatic heterogeneous electron transfer reactions between a donor/acceptor ion in solution and a metal electrode. The quantum solvent free energy curves for the reaction will be computed, and quantum transition state theory used to calculate the electron transfer rate constant. Preliminary studies in which the water solvent model has been quantized suggest that the solvent activation free energy barrier and thermodynamic driving force for the electron transfer process can be significantly influenced by quantum effects. In both cases, the computational requirements are massive, representing Grand Challenge-level efforts. Moreover, both projects involve the application of novel theoretical methodologies to simulate complex dynamical phenomenon in condensed matter.